Graph theory with applications in chemistry
Organizer and Chair: Patrick Fowler
(University of Sheffield) and Wendy Myrvold
(University of Victoria)
- GUNNAR BRINKMANN, Universiteit Gent
Existence and Construction of Nanojoins [PDF]
A nanojoin is a part of a carbon molecule that connects two or more
halftubes (halfs of fullerene nanotubes) with the same or
different parameters, sometimes giving a molecule with promising
electrical properties. Nanojoins are modeled as plane graphs with 2
or more special faces -- to attach the tubes -- and
all the remaining faces hexagons, heptagons or pentagons. Vertices not
in a special face have degree 3. We will answer the question for
which tube geometries and pentagon/heptagon combinations nanojoins
exist and give results of a program for exhaustive generation of
nanojoins. Coauthors: Dieter Mourisse and Leanne Rylands.
- PATRICK FOWLER, The University of Sheffield
Graph Theory on the Edge of Chemistry: Perimeter Currents and Bond Orders [PDF]
Visualisation of current patterns induced in carbon frameworks by
magnetic fields gives insight into
Conjugated-circuit models offer a way to estimate currents in benzenoids
that is conceptually simple, if laborious in practice. (Conjugated circuits are cycles C in the
graph G such that both C and G-C have perfect matchings.)
A simple connection between Pauling bond order
(ratio of edge matching number to number of perfect matchings of the graph)
and perimeter currents of benzenoids is described. Inversion of the adjacency matrix gives full current maps for Kekulean benzenoids without internal hexagons.
This is joint work with Wendy Myrvold.
- JACK GRAVER, Syracuse University
Fries chains in a fullerene [PDF]
The Clar chains, introduced by Hartung, describe the Kekule structure that gives Clar number of a fullerene. In this paper, we develop Fries chains, the analogue to the Clar chains that describe the Kekule structure giving the Fries number of a fullerene.
- ELIZABETH HARTUNG, Massachusetts College of Liberal Arts
The Clar number and Kekule Count of Benzenoids [PDF]
The Kekule count, the number of perfect matchings, and the Clar number, the maximum number of independent hexagonal rings, are two parameters related to the stability of benzenoid molecules. This talk will describe some results on the Clar number for classes of benzenoids. We will also introduce a family of pairs of benzenoids on the same number of vertices such that for each pair, one has a larger Clar number and the other a higher Kekule count.
- WENDY MYRVOLD, University of Victoria
Graph Theoretic Models for Ring Currents [PDF]
The Randic current model describes ring currents induced in benzenoids by external magnetic fields in terms of contributions from conjugated circuits (cycles C in the graph G such that both C and G-C have perfect matchings). We propose improvements to the Randic current predictions for cases where the graph has edges that are not in any perfect matchings. In these cases, there are regions of the molecule where current flows, but the Randic model is predicting that there is no current. We also investigate extensions that predict current for graphs that have no perfect matchings. Joint work with Patrick Fowler.